math111_logo Composition and Matrix Multiplication


Exercise Compute matrix products.

Answer

[ 1 1 ][ 1/2 1/2 ] = [ 1 0 ]
1 -1 1/2 -1/2 0 1
[   ] [ 8 ] = [   ]
  7  
1 -2 3 -4 5 6 12
  5  
  4  
[ 8 ] [   ] = [ 8 -16 24 -32 40 ]
7   7 -14 21 -28 35
6 1 -2 3 -4 5 6 -12 18 -24 30
5   5 -10 -15 -20 25
4   4 -8 12 -16 20
[ 1 -2 3 ]
-2 3 -4
[ -2 -1 ]
0 1
1 1
=
[ 1 0 ]
0 1
[ -2 -1 ]
0 1
1 1
[ 1 -2 3 ]
-2 3 -4
=
[ 0 1 -2 ]
-2 3 -4
-1 1 -1
[ -2 -1 ][ 1 -2 3 ] = [ 0 1 -2 ]
0 1 -2 3 -4 -2 3 -4
[ 1 2 3 4 ]
5 6 7 8
9 10 11 12
[ 1 1 ]
-1 -1
1 -1
-1 1
=
[ -2 0 ]
-2 0
-2 0
[ 1 -1 1 ][ 1 2 3 4 ] = [ 5 6 7 8 ]
-1 2 -1 5 6 7 8 0 0 0 0
2 0 -1 9 10 11 12 -7 -6 -5 -4